The simple modules of certain generalized crossed products

Abstract

We consider a Dedekind domain D and a Z-graded ring R = ⊕ i ∈ Z Ri with Ro = D and each Ri = Dυi being a free D-module of rank 1. The structure of R is described by an automorphism of D and a generalized 2-cocycle c : Z × Z → D not necessarily taking its values in the units of D. The aim of this paper is to classify the simple R-modules, say in the case where c(i, j) ≠ 0 for all i, j ∈ Z. We also deal with this problem in the N-graded case. As a consequence we obtain a description of the simple modules of some classical algebras and of generalized Weyl algebras. © 1997 Academic Press.